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Under police questioning not long after his pregnant wife and young daughters vanished from their Colorado home earlier this month, Chris Watts allegedly admitted he strangled his spouse, Shanann Watts — but he gave a startling reason for doing so.

According to an arrest affidavit obtained by PEOPLE, Chris allegedly said that after he told Shanann, 34, he wanted to separate, he saw her strangling their 3-year-old, Celeste, while their 4-year-old, Bella, lay “blue” and apparently lifeless nearby.

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In response, Chris allegedly claimed, he “went into a rage” and strangled Shanann.

But authorities aren’t buying his shocking explanation. On Aug. 15, two days after Shanann and the girls were reported missing and hours before the announcement that their bodies had been found on the property of Chris’ former employer, he was arrested.

The 33-year-old faces charges of first-degree murder in all three deaths, among other charges.

A source close to the investigation tells PEOPLE that Chris’ alleged defense is not plausible.

“There is absolutely no evidence that she killed her children,” the source tells PEOPLE in this week’s issue. “None at all. And there is physical evidence to tie him to their murders. Strangulation is a very personal way to kill someone, with a lot of physical contact. Just based on the preliminary evidence, everything is consistent with him killing them all.”

• For more on the shocking killings of Shanann Watts and her two young daughters, subscribe now to PEOPLE or pick up this week’s issue, on newsstands Friday.

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